%%%-------------------------------------------------------------------
%%% File    : p11.erl
%%% Author  : Plamen Dragozov <plamen at dragozov.com>
%%% Description : 
%%% In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
%%% 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
%%% 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
%%% 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
%%% 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
%%% 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
%%% 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
%%% 32 98 81 28 64 23 67 10[26]38 40 67 59 54 70 66 18 38 64 70
%%% 67 26 20 68 02 62 12 20 95[63]94 39 63 08 40 91 66 49 94 21
%%% 24 55 58 05 66 73 99 26 97 17[78]78 96 83 14 88 34 89 63 72
%%% 21 36 23 09 75 00 76 44 20 45 35[14]00 61 33 97 34 31 33 95
%%% 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
%%% 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
%%% 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
%%% 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
%%% 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
%%% 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
%%% 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
%%% 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
%%% 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
%%% 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
%%% The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
%%% What is the greatest product of four adjacent numbers in any direction 
%%% (up, down, left, right, or diagonally) in the 20×20 grid?
%%%
%%% Created :  2 Dec 2008
%%%-------------------------------------------------------------------
-module(p11).

%% API
-compile(export_all).

%%====================================================================
%% API
%%====================================================================
%%--------------------------------------------------------------------
%% Function: solution(Matrix, Width, SubWidth) -> int()
%% Description: Return the maximum product of a submatrix of size 
%% SubWidth.
%%--------------------------------------------------------------------
solution(Matrix, Width, SubWidth) ->
    %iterate through all submatrices and calculate the maximum product
    SubProduct = fun(Row, _, Max, _) when Row > Width - SubWidth ->
                         Max;
                    (Row, Column, Max, Funself) when Column > Width - SubWidth->
                         Funself(Row + 1, 0, Max, Funself);
                    (Row, Column, Max, Funself) ->
                         Sub = submatrix(Matrix, Width, Row, Column, SubWidth),
                         MaxP = max_product(Sub, SubWidth),
                         NewMax = case MaxP > Max of
                                      true ->
                                          MaxP;
                                      _ -> Max
                                  end,
                         Funself(Row, Column + 1, NewMax, Funself)
                 end,
    SubProduct(0, 0, 0, SubProduct).

test()->
    M = [08,02,22,97,38,15,00,40,00,75,04,05,07,78,52,12,50,77,91,08,
         49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,04,56,62,00,
         81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,03,49,13,36,65,
         52,70,95,23,04,60,11,42,69,24,68,56,01,32,56,71,37,02,36,91,
         22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80,
         24,47,32,60,99,03,45,02,44,75,33,53,78,36,84,20,35,17,12,50,
         32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70,
         67,26,20,68,02,62,12,20,95,63,94,39,63,08,40,91,66,49,94,21,
         24,55,58,05,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72,
         21,36,23,09,75,00,76,44,20,45,35,14,00,61,33,97,34,31,33,95,
         78,17,53,28,22,75,31,67,15,94,03,80,04,62,16,14,09,53,56,92,
         16,39,05,42,96,35,31,47,55,58,88,24,00,17,54,24,36,29,85,57,
         86,56,00,48,35,71,89,07,05,44,44,37,44,60,21,58,51,54,17,58,
         19,80,81,68,05,94,47,69,28,73,92,13,86,52,17,77,04,89,55,40,
         04,52,08,83,97,35,99,16,07,97,57,32,16,26,26,79,33,27,98,66,
         88,36,68,87,57,62,20,72,03,46,33,67,46,55,12,32,63,93,53,69,
         04,42,16,73,38,25,39,11,24,94,72,18,08,46,29,32,40,62,76,36,
         20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,04,36,16,
         20,73,35,29,78,31,90,01,74,31,49,71,48,86,81,16,23,57,05,54,
         01,70,54,71,83,51,54,69,16,92,33,48,61,43,52,01,89,19,67,48],
    solution(array:from_list(M), 20, 4).


%%====================================================================
%% Internal functions
%%====================================================================

%Find the maximum product in a matrix M of size Size 
max_product(M, Size) ->
    Horisontal = fun(_, Column, Acc, _) when Column >= Size ->
                         Acc;
                    (Row, Column, Acc, Funself) -> 
                         Funself(Row, 
                                 Column + 1, 
                                 array:get(Row*Size + Column, M)*Acc,
                                 Funself)
                 end,
    Vertical = fun(Row, _, Acc, _) when Row >= Size ->
                       Acc;
                  (Row, Column, Acc, Funself) -> 
                       Funself(Row + 1, 
                               Column, 
                               array:get(Row*Size + Column, M)*Acc,
                               Funself)
               end,
    Diagonal = fun(_, Row, _, Acc, _) when Row >= Size ->
                       Acc;
                  (left, Row, Column, Acc, Funself) ->
                       Funself(left, 
                               Row + 1, 
                               Column + 1, 
                               array:get(Row*Size + Column, M)*Acc,
                               Funself);
                  (right, Row, Column, Acc, Funself) ->
                       Funself(right, 
                               Row + 1, 
                               Column - 1, 
                               array:get(Row*Size + Column, M) * Acc,
                               Funself)
               end,
    MaxHV = fun(I, Max, _) when I >= Size -> 
                    Max;
               (I, Max, Funself) ->
                    H = Horisontal(I, 0, 1, Horisontal),
                    V = Vertical(0, I, 1, Vertical),
                    Max1 = case H > V of
                               true ->
                                   H;
                               _ -> V
                           end,
                    NewMax = case Max1 > Max of 
                                 true ->
                                     Max1;
                                 _ -> Max
                             end,
                    Funself(I + 1, NewMax, Funself)
            end,
    MaxD = fun()->
                   D1 = Diagonal(left, 0, 0, 1, Diagonal),
                   D2 = Diagonal(right, 0, Size - 1, 1, Diagonal),
                   case D1 > D2 of
                       true ->
                           D1;
                       _ -> D2
                   end
           end,
    Max1 = MaxHV(0, 0, MaxHV),
    Max2 = MaxD(),
    case Max1 > Max2 of
        true ->
            Max1;
        _ -> Max2
    end.

%Returns the submatrix of size Size at the position X,Y in the big matrix M.
%Matrices will be 0 based!
submatrix(M, BigSize, X, Y, Size) ->
    Copy = fun(Row, _Column, Acc, _) when Row >= Size-> 
                   Acc; 
              (Row, Column,  Acc, Funself) when Column >= Size ->
                   Funself(Row + 1, 0, Acc, Funself);
              (Row, Column,  Acc, Funself) -> %arrays are 0 based in Erlang
                   SrcPos = (Y + Row) * BigSize  + X + Column,
                   DestPos = Row*Size + Column,
                   Value = array:get(SrcPos, M),
                   Acc1 = array:set(DestPos, Value, Acc),
                   Funself(Row, Column + 1, Acc1, Funself)
           end,
    Copy(0, 0, array:new(Size*Size), Copy).
